High-resolution methods for flow regime transitions at canal structures.

摘要

A mathematical approach for handling changing flow regimes at canal gate structures was developed. The characteristic method was used in conjunction with high resolution Riemann solvers linked with total variation diminishing (TVD) limiters. The methods were compared to the Godunov first order method, a second order upwind method, a Modified Lax-Wendroff Method coupled with the specified interval method at the boundaries, and a Preissmann implicit scheme method. The TVD limiters applied in this study were SUPERBEE, van Albada, van Leer, and MINMOD. Twelve different cases of flow regime changes in a canal of two reaches with different bed slopes with a gate downstream of the first and a weir downstream of the second were tested. Simulation results were compared in terms of differences in spatial and temporal values of depth and velocity. While the Godunov method was diffusive, the second order non-monotone upwind method produced numerical oscillations in unsteady regions. The Modified Lax-Wendroff method with the specified interval method at the boundaries failed to give acceptable results. The implicit method gave smoother results than the other methods. The approximate Riemann Solver-TVD method was robust in terms of minimizing the spurious oscillations generated during changing flow regimes, whether from orifice to non-orifice, or from free to submerged, and vice versa. The approach developed was able to resolve shocks and contacts successfully.